/BEM/FLOW
Block Format Keyword Describes the incompressible fluid flow by boundary elements method.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/BEM/FLOW/flow_ID/unit_ID  
flow_title  
surf_ID_{ex}  N_{io}  I_{inside}  fct_ID_{fsp}  Fscale_{fsp}  Ascale_{fsp}  
grn_ID_{aux}  I_{test}  Tole  
Rho  I_{vinf} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

surf_ID_{io}  fct_ID_{nv}  fct_ID_{p}  Fscale_{nv}  Fscale_{p}  Ascale_{t} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

I_{form}  I_{pri}  Dt_{flow}  
fct_ID_{v}  Fscale_{v}  Ascale_{v}  
Dir_{x}  Dir_{y}  Dir_{z} 
Definition
Field  Contents  SI Unit Example 

flow_ID  Incompressible flow block
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

flow_title  Incompressible flow block
title. (Character, maximum 100 characters) 

surf_ID_{ex}  Flow external surface
identifier. (Integer) 

N_{io}  Number of inflowoutflow
surfaces. (Integer) 

I_{inside}  Inside or outside flow flag.
(Integer) 

fct_ID_{fsp}  Stagnation pressure curve
identifier. (Integer) 

Fscale_{fsp}  Stagnation pressure scale
factor. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Ascale_{fsp}  Abcissa scale factor for
stagnation pressure curve. Default = 1.0 (Real) 
$\left[\text{s}\right]$ 
grn_ID_{aux}  Auxiliary nodes group
identifier. 2 (Integer) 

I_{test}  Test auxiliary nodes flag.
2 (Integer > 0) 

Tole  A dimensional tolerance.
2 Default = 1.e5 (Real) 

Rho  Fluid
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
I_{vinf}  Additional velocity field
flag. 3 (Integer > 0) 

surf_ID_{io}  InflowOutflow surface
identifier. 4 (Integer) 

fct_ID_{nv}  Normal velocity curve.
4 (Integer) 

fct_ID_{p}  Imposed pressure curve.
5 (Integer) 

Fscale_{nv}  Normal velocity scale
factor. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
Fscale_{p}  Imposed pressure scale
factor. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Ascale_{t}  Abscissa scale factor for
normal velocity curve and imposed pressure curve. Default = 1.0 (Real) 
$\left[\text{s}\right]$ 
I_{form}  Formulation flag. 6
(Integer > 1) 

I_{pri}  Output level. (Integer > 1) 

Dt_{flow}  Time step for BEM matrices
assembly. 7
(Real) 
$\left[\text{s}\right]$ 
fct_ID_{v}  Velocity curve
identifier. (Integer) 

Fscale_{v}  Velocity scale
factor. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
Ascale_{v}  Abscissa scale factor for
velocity curve. Default = 1.0 (Real) 
$\left[\text{s}\right]$ 
Dir_{x}  X component of the
additional field direction vector. (Real) 

Dir_{y}  Y component of the
additional field direction vector. (Real) 

Dir_{z}  Z component of the
additional field direction vector. (Real) 
Example
#12345678910
/BEM/FLOW/1
Flow 1
#surf_IDex Nio Iinside fct_IDfsp Fscale_fsp Ascale_fsp
3 2 1 0 0. 0.
#grn_IDaux Itest Tole
1 0 1e5
# Rho Ivinf
1.0 0
#surf_IDio fct_IDnv fct_IDp Fscale_nv Fscale_p Ascale_t
2 1 0 10.0 0.0 1.0
#surf_IDio fct_IDnv fct_IDp Fscale_nv Fscale_p Ascale_t
1 0 1 0.0 101325.0 1.0
# Iform Ipri Dt_flow
1 1 1e3
#12345678910
/FUNCT/1
Function 1
# X Y
0 1
100 1
#12345678910
#enddata
Comments
 The surf_ID_{ex} must define a closed surface.
 Using BEM, the flow
potential, velocity and pressure are computed for nodes belonging to the surface
defined by surf_ID_{ex}.
For visual and posttreatment concerns, the flow characteristics can be computed for a set of nodes inside the flow belonging to grn_ID_{aux}.
If I_{test} = 1, whether the auxiliary nodes are actually located inside (if I_{inside} =1) or outside (if I_{inside} =2), the surface defined by surf_ID_{ex} at each time step is tested. Incorrect nodes are then canceled for the current time step.
Tolerance Tole is used to perform the pointinsideclosedsurface test.
 Flag
I_{vinf} is only effective
for flow computation in an unbounded domain outside the surface defined by
surf_ID_{ex}
(I_{inside}
=2).
If I_{vinf} = 1, an inflow condition is defined by an additional homogeneous flow defined in free space. The computed flow will be identical to the additional flow at an infinite distance from the surface defined by surf_ID_{ex}.
 If
I_{inside} =
0: Flow is computed inside the surface defined by
surf_ID_{ex}. There must be at
least one surface where the normal velocity is imposed and only one surface
where the normal velocity could be left as free. The velocity at the free
surface will be computed thanks to flux equilibrium on the global surface
defined by surf_ID_{ex}.
If I_{inside} = 2 and I_{vinf} = 0: I_{inside} = 0 but flow is computed outside the surface defined by surf_ID_{ex}.
If I_{inside} = 2 and I_{vinf} = 1: numbers of surface could be free and the normal velocity must be imposed on all of them.
 In order to reduce pressure from the velocity field, one and only one pressure must be imposed for the entire flow computation: it can be either the global stagnation pressure or the pressure at one of the inflowoutflow surfaces.
 The collocation approach is
faster but may not be robust enough to handle very complex geometries.
The Galerkin approach works in every situation but is significantly slower.
 BEM matrices depend only on
the geometry of the surface.
If Dt_{flow} = 0 (default), they are assembled at every cycle of the simulation (the time step being classically given by the stability condition of finite elements).
If Dt_{flow} ≠ 0: max(Dt_{flow}, Dt) is used to update to BEM matrices; where Dt is the finite element time step.